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Trevor D. Smith 1
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Comprehensive Recalibration for WEAP of the LRFD Pile 7
Resistance Factor Under Initial and Restrike Conditions 8
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Trevor D. Smith1
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16 1Professor of Civil Engineering, Department of Civil and Environmental Engineering, Portland State University, PO 17
Box 751, Portland, OR 97207; Phone: 503-725-3225; [email protected] 18
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Submission Date: November 4, 2011 24
Words in Text: 5479 25
Tables: 5 26
Figures: 3 27
Total Word Count: 7479 28
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TRB 2012 Annual Meeting Paper revised from original submittal.
Trevor D. Smith 2
ABSTRACT 1 The Oregon Department of Transportation (ODOT) uses the DRIVEN pile capacity software and Wave Equation 2
Analysis of Piles (WEAP) software for controlling driving stresses and establishing field resistance from the bearing 3
graph. Typically, ODOT piles exhibit set-up after the end of initial driving (EOID), and ODOT may restrike. For 4
this WEAP Load Resistance Factor Design (LRFD) resistance factor recalibration, a new database was formed by 5
culling existing databases, including the Deep Foundation Load Test Database (DFLTD) and NCHRP507’s 6
PDLT2000 database. The resulting information was merged with 166 new cases to create a new comprehensive 7
database. Neither DFLTD nor PDLT2000 databases proved correct after crosschecking with other sources. Some 8
cases contained serious errors. The largest source of anomalies and missing data was the blow count, especially at 9
the beginning of restrike (BOR). Input Tiers and Output Ranks were designed to assist in data qualifying, ranking 10
data quality, and statistical profiling for calibration at EOID and BOR. One hundred seventy-five piles supplied 11
quality data for WEAP resistance prediction, which generated Davisson’s mean bias and coefficient of variation 12
statistics for recalibration. Bias is compared to that reported in NCHRP507, and a study of variables including blow 13
count ranges, artificial removal of outliers, and soil type differences is presented. First Order Second Moment 14
resistance factors are given at EOID and BOR for ten scenarios. Advanced Monte Carlo procedures, with random 15
number generation and lognormal tail fits, provide EOID and BOR resistance factors to form a basis for future 16
implementation of five ODOT scenarios. 17
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TRB 2012 Annual Meeting Paper revised from original submittal.
Trevor D. Smith 3
BACKGROUND 1
The Problem and ODOT Concerns 2 Given the level of research activity by transportation departments (1), adoption of Load and Resistance Factor 3
Design (LRFD) principles for pile foundations has been difficult. These difficulties include establishing resistance 4
factors, φ, for dynamic methods that address local implementation needs and that capture local practice. The bridge 5
section of the Oregon Department of Transportation (ODOT) routinely uses the Wave Equation Analysis of Piles 6
(WEAP) (2) for both driving control and capacity during initial driving (EOID) and occasionally at the beginning of 7
restrike (BOR) condition. American Association of State Highway and Transportation Officials (AASHTO) codes 8
(3, 4, 5) attempt to provide a basis for uniform implementation of LRFD principles, but offer no discussion in the 9
current code to clarify the EOID and BOR decisions for WEAP (5). AASHTO has never offered a separate φ at 10
BOR conditions for WEAP. 11
LRFD methodology at the ultimate limit state calls for load, Qij, to be increased by load factors, γij, 12
assigned to the load source (e.g. dead, live, wind) and compared to a reduced nominal resistance, Rnk, employing a 13
resistance factor, φ. The inequality to be satisfied in LRFD-based design is Eq. 1. 14
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nk kij i j Rφ Qγ (1) 16
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Since Qij and Rnk are random variables, the φk calibration to foundation design uses a Reliability Index 18
value, β, to quantify risk for the foundation. Most dynamic methods trace the origins of their AASHTO φ values to 19
the NCHRP507 work by Paikowsky et al. (6), who discussed dead load to live load ratios, site variability, pile 20
redundancy, soil types, and the quality effects of dynamic testing for pile acceptance. The mean bias, λ, used 21
Davisson’s criteria and reliability index values, β, of 2.33 and 3.0 for redundant and non-redundant piles 22
respectively. Based on pile cases from across the country, NCHRP507 provided the basis for the past AASHTO 23
codes’ (3, 4) WEAP φ at 0.4 for redundant piles. 24
ODOT only occasionally conducts pile load testing, and the use of dynamic testing with signal matching 25
technology, employing the higher φ of 0.65, is cost-prohibitive for many bridge contracts. A 2008 survey by Smith 26
and Dusicka (7) assessed both the overall use of WEAP in Northwest DOT practice and the effects of applying the 27
then-current AASHTO-approved WEAP φ factor to bridge designs at EOID. The survey’s results showed a strong 28
opinion among DOT practitioners to support increasing φ when used at EOID to capture pile resistance. Summary 29
findings included: 30
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60 percent of Northwest DOTs utilized WEAP, often at EOID and BOR 32
80 percent of Northwest DOTs considered φ at 0.4 to be conservative 33
750 bridges were expected to be designed for the Northwest in the next 10 years 34
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The survey results found strong support for an LRFD resistance factor recalibration effort for WEAP. 36
Piles often show long-term capacity gains, called set-up. Under these conditions, the use of driving blow 37
counts at EOID could yield conservative resistance results, and the pile could be restruck after a waiting period to 38
give a more representative BOR blow count. The ODOT has generally followed all WEAP recommendations 39
contained in current Federal Highway Administration (FHWA) manuals (8) for pile design and in code requirements 40
set by AASHTO, but judged by the low φ value, the AASHTO declares the popular WEAP method used throughout 41
the Northwest to be one of the least reliable. Foundation conditions throughout the heavily populated Willamette 42
Valley and the Portland metropolitan area are predominantly sand, silt, and clay, in which friction piles are known to 43
exhibit set-up after EOID. Without φ at BOR available for WEAP, post set-up BOR blow counts cannot be used 44
with any statistical confidence. Past state studies reporting φ recalibrations have drawn extensively from their own 45
load tests, often using static methods or dynamic signal matching (1, 9, 10), and thus have their own DOT practice 46
standard embedded in the calibration. 47
The FHWA (8) endorses the dual use of the DRIVEN software (11) to calculate the pile static capacity 48
distribution and to format the input file for WEAP, which then provides the bearing graph consistent with EOID and 49
BOR conditions. DRIVEN performs static analysis computations utilizing Tomlinson’s Alpha method (12) for 50
cohesive soil and Nordlund’s method (13, 14) for cohesionless soil. Establishing resistance from WEAP becomes 51
difficult with the large number of site-specific variables, modeling complexities, and sensitivity of the output to all 52
driving components, particularly the hammer efficiency. Hammer type is selected in WEAP from pull-down menus, 53
with hammer model details and performance information found in the WEAP library. For this study, DRIVEN and 54
WEAP were set to use default parameters, and all FHWA recommendations were diligently followed in providing 55
TRB 2012 Annual Meeting Paper revised from original submittal.
Trevor D. Smith 4
resistances at EOID and BOR conditions. Unless field records provided a different parameter, e.g. thickness and 1
type of hammer cushion, only default values for all hammer accessories and the helmet weight were used. Side 2
damping coefficients are different between soil types. Therefore, in layered soils, the WEAP side damping 3
coefficient was set to a weighted average value based on the individual layer’s DRIVEN-predicted contribution. 4
5
MASTER DATABASE CONSTRUCTION AND QUALITY REVIEW 6 The quantity and quality of information required for WEAP analysis is considerable. The first key task for this 7
study was to build and validate a detailed case history database to offer high recalibration confidence (15). ODOT 8
provided two databases as the primary sources to begin gathering pile histories: PDLT2000 (6) and FHWA’s Deep 9
Foundation Load Test Database (DFLTD) (16). In addition, the Florida DOT provided their FL Database and 10
Professor Jim Long the FHWA Database (9). Additional case histories and DOT reports were also used to produce a 11
high-quality, WEAP purpose-designed case history set called the Full PSU Master Database for EOID and BOR φ 12
recalibration (15). All additional data helped ensure high confidence for this effort by increasing the sample size, 13
allowing crosschecks for error detection, and resolving anomalies. The DFLTD consists of over 1,000 load tests 14
conducted on driven and drilled foundations, gathered and updated by FHWA over a 15-year period. The 15
information includes soil boring logs, laboratory data, pile driving logs, and the field load test result. The 16
PDLT2000 database, compiled by Paikowsky (17) from approximately 77 different project sites, was used for all the 17
dynamic-method φ values contained in NCHRP507. The database contained 389 driven pile cases, of which a total 18
of 210 showed driving times and pile details. Among these were 83 piles with driving data at the time of both EOID 19
and BOR and 73 cases with BOR only, thus offering an EOID plus BOR “qualified” matched total of 156 pile cases 20
(provided missing EOID data could be located). Complete soil information for each layer, pile driving logs, the 21
clock time delay from EOID to BOR, or the static load test result does not exist in PDLT2000 for the 156 piles. 22
These are significant omissions when attempting DRIVEN and WEAP analyses for capacity. The research team 23
expended considerable effort to secure missing data. 24
The “build rationale” for the Full PSU Master Database was set to ensure a reasonable match by pile and 25
soil breakdown, to ODOT bridge foundations. The DFLTD also provided additional case histories not contained in 26
PDLT2000. These piles, together with an extensive review of recent geotechnical literature and requests to various 27
DOTs, added a total of 166 new EOID and BOR qualified case histories. Typically, private consultant load tests and 28
most agency-published case histories rarely contain sufficient information for full analysis; however, the data was 29
included in the Full PSU Master Database, which reached a total of 322 piles. The largest state contributors were 30
Florida at 53, South Carolina at 23, Louisiana at 22, and Wisconsin at 14, with a remaining 24 states contributing 31
less than 10 cases each (15). Each soil layer’s contribution to resistance was examined and a general soil type 32
category was assigned for ease of organization. Cohesive soils contributing more than 80 percent of a pile’s capacity 33
were designated Clay cases. Cohesionless soils contributing more than 80 percent of a pile’s capacity were 34
designated Sand cases. Layered soil cases, between these brackets, were called Mixed cases. 35
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Data Anomalies and Cross Checking 37 There were parameters for which PDLT2000 was found to be consistently erroneous when compared to the values 38
recorded for the same pile in other databases and in other original source reports. These included the pile blow 39
count, pile length, and the penetration depth. After comparison with other original source data, DFLTD was also 40
shown to have anomalies, likely caused by simple input key-stroke mistakes during data compilation from the large 41
number of project sites. The DFLTD pile driving records contain no calendar or clock time delay for restrike. Cross-42
examinations of DFLTD and PDLT2000 showed that a total of 72 of the 156 qualified piles in PDLT2000 had 43
anomalies (with 29 piles having no site identifier for any follow-up investigation). Twenty-eight piles had more than 44
one anomaly, especially the BOR blow count. After resolution of errors and anomalies, 103 of the 156 PDLT2000 45
entries qualified for DRIVEN and WEAP final analysis. In cases where piles from the PDLT2000 were matched 46
with piles in the DFLTD by a site identifier, soil data was obtained from DFLTD. 47
It is essential that the most accurate data be used for reliable φ calibration. Due to the numerous times in 48
which a value from the PDLT2000 disagreed with a value from the DFLTD and was also proven erroneous by the 49
consistent approach of matching the pile record to another database (or even original documents such as driving 50
logs), the most reliable source was judged to be DFLTD. 51
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DATABASE EXAMINATION AND QUALITY METRICS 53 Allen et al. (18) makes clear that for quality LRFD calibration, the statistical quantity and quality of pile data must 54
be assessed. Each pile case history included in the Full PSU Master Database was assigned an Input Tier number (1 55
down to 3) that described the level of reliance on input assumptions to analyze the case in both DRIVEN and 56
TRB 2012 Annual Meeting Paper revised from original submittal.
Trevor D. Smith 5
WEAP. A pile case with the most complete set of input parameters was assigned to Tier 1, and a pile case history 1
with the most incomplete set of input parameters, which could not be analyzed without the missing key information 2
(e.g. pile blow count, N), was assigned to Tier 3. 3
After DRIVEN and WEAP were completed at EOID and BOR, each case history output was assigned a 4
qualitative Output Rank, from 1 to 4, designed to record analysis confidence levels, tag for critical assumptions, and 5
flag problematic cases for further examination. The Input Tier and Output Rank structure assisted in 6
troubleshooting problematic cases and helped address trends that showed up during statistical analysis. A summary 7
of the input and output quality rubrics is presented in Table 1. 8
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TABLE 1 Case History Input and Output Rubric 10
Category Definition
Input
Tier 1
Very
Good
a
Full soil data is reported, including measured shear strengths. Hammer type and driving
accessory details are known. All pile information is known including composition, size, and
driving state (plugged or unplugged). Davisson’s resistance and signal matching-based
resistance is available. No anomalies are reported in either the boring log or driving log that
might significantly affect prediction.
b All criteria is met for Tier 1a except no signal matching-based resistance information is
reported, or pile is driving harder with 10 BPI < N < 15 BPI.
c Possible relaxation detected with blow count EOID > BOR and should be confirmed, or
very hard driving with N >15 BPI.
Input
Tier 2
Good
a
DRIVEN can be performed; WEAP cannot be routinely performed without assumptions. All
pile and hammer information and details are known, but there are anomalies to resolve and data
missing. Some soil strength properties known and other key properties are known.
b
Typically neither DRIVEN nor WEAP can be routinely performed. All criteria are met for Tier
2a, except assumptions on cohesive soil shear strength values are required, or there is a lack of
water table information for granular soil.
Input Tier 3
Poor
No soil data or hammer information known. Non-typical soil types, e.g. sandstone. No field
blow counts or load test results are available.
Output Rank 1
Good
No key assumptions were required for analysis and no anomalies present in output. Typically, in
soft soils, WEAP resistance approximately equals DRIVEN resistance, and for harder soils
WEAP resistance is less than DRIVEN resistance.
Output Rank 2
Acceptable
Possible minor anomalies present or non-critical assumptions were made, e.g. hammer type not
clear but matched from WEAP library, assumed water table in sand, WEAP resistance greater
than signal-matching resistance. Davisson’s criteria is significantly greater than the DRIVEN
resistance.
Output Rank 3
Poor
No hammer cushion match. Significant anomalies. Pile showed relaxation on BOR. Bearing
graph overly sensitive to damping and/or the side friction to total resistance percent distribution.
Output Rank 4
Ineligible
Lacking information to generate case bias, λ, e.g. lacking Davisson’s criteria or the field blow
count.
11
Approximately one-third of the original 156 qualified piles identified in PDLT2000 had insufficient data for 12
satisfactory DRIVEN and WEAP analysis and were in Input Tier 3. Coincidentally, one-third of the final 322 piles 13
in the Full PSU Master Database were also in Tier 3. The 322 cases in the Full PSU Master Database had 179 14
qualified cases in input Tier 1 and Tier 2 to produce φ, 80 percent more than used by Paikowsky (6) and 15
considerably larger than data samples in any other reported recalibrations by WEAP. Table 2 shows the breakdown 16
by pile type and soil type of the 322 piles. 17
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TRB 2012 Annual Meeting Paper revised from original submittal.
Trevor D. Smith 6
TABLE 2 Breakdown of All 322 Piles in the Full PSU Master Database by Pile and Soil Type 1
Major Contributing
Soil Type
Pile Type
Total Cases
Concrete
Pile H-Pile
Closed End
Pipe Pile
Open Ended
Pipe Pile Other
Sand 62 19 17 4 1 103
Clay 17 5 10 1 0 33
Mix 14 9 16 5 1 45
Unknown 54 24 38 20 5 141
Total Cases 147 57 81 30 7 322
2
As 81 cases had calendar and clock time known at the time of both EOID and BOR driving, as well as the 3
calendar time for the static load test, a subset of cases was created where restrike or load testing may have occurred 4
either too early or too late for representative set-up to occur. Further, 84 piles reported multiple restrike blow series, 5
but few qualified for DRIVEN and WEAP analysis. Thus all BOR calibrations were conducted on the first restrike 6
blow series only. 7
8
BEARING RESISTANCE EVALUATION, STATISTICAL PROFILING AND FILTERS 9
Subsurface Information Quality, Pile Blow Count Anomalies, and Modeling 10 The DRIVEN program requires a relatively modest amount of soil information, including water table, soil unit 11
weight, and strength parameters for soils. For those piles with soil profile data, there were often key parameters 12
absent, and certain assumptions had to be made. Laboratory data for soil strength parameters was rarely present in 13
the DFLTD which consisted predominantly of results from the standard penetration test (SPT) for DRIVEN use. For 14
this study, Smith et al. (15) gives full details of the approach described by FHWA (8) for creating representative 15
granular soil friction angles and cohesive soil undrained strengths from the SPT. A large variation in EOID and 16
BOR pile blow counts, calendar times, and field piling practice norms exists in the database. For the purposes of 17
WEAP resistance factor calibration and to assist implementation, the inherent variability of national DOT standards 18
is captured in the Full PSU Master Database by keeping a high-quality and inclusive database. 19
The DFLTD has no consistent separation between EOID and BOR blow counts, but does present the 20
complete driving record. It was assumed that the integer one-foot depth intervals values in DFLTD were for initial 21
driving and the decimal values were for restrike. Then, blows given by the decimal feet interval format indicated 22
restrike had begun, and the data represented an equivalent number of the blows per foot (BPF). After the separation 23
between EOID and BOR, 16 of the 74 matched piles showed the blows at EOID and BOR, reported in both 24
databases, were exactly the same, while others were close. Changes in pile blow count indicate changes in 25
resistance based on the bearing graph. However, different bearing graphs for EOID and BOR can result from 26
hammer changes and/or substitutions of a well-used stiffer cushion on concrete piles endorsed by FHWA (8). A 27
slight reduction in blow counts at BOR, for the same hammer but with a stiffer cushion, may not necessarily indicate 28
relaxation by WEAP as the bearing graph will change. 29
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Sample Population Analysis and Outliers 31 This recalibration effort utilized the ratio between Davisson’s load test criteria and the corresponding EOID and 32
BOR resistance predictions from WEAP to calculate λ bias defined in Eq. 2. 33
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Therefore, a pile λ value less than 1 is an unconservative WEAP prediction and greater than 1 is a conservative 36
prediction, compared to Davisson’s measurement. The average λ from a sample of case histories is called the 37
sample bias and is often designated λR for resistance factor calculation; hereafter, this is termed λ for the full sample 38
statistical mean bias. Recognizing the frequent DRIVEN and WEAP assumptions and interpretation decisions, a 39
statistical comparison was made between the 91 matched piles in the Full PSU Master Database with the 99 pile 40
case histories reported by NCHRP507 (contained in the PDLT2000 Master). The 99 cases were assumed to contain 41
well-defined case histories, which would have placed them all in Tier 1 or Tier 2 for this study. NCHRP507 reports 42
EOID mean λ bias, standard deviation (s.d.) and coefficient of variation (COV) of 1.656, 1.199, and 0.724 43
λ = Davisson’s criteria resistance (2)
Predicted WEAP resistance
TRB 2012 Annual Meeting Paper revised from original submittal.
Trevor D. Smith 7
respectively, and the 91 matched piles from the Full PSU Master Database at EOID had λ, s.d., and COV of 1.661, 1
1.264, and 0.761 respectively. 2
Significant discrepancies in a WEAP resistance prediction can arise from erroneous reporting of field blow 3
count, which was the largest single source of anomalies reported between source databases. Errors on the blow 4
count low side reduce predicted resistance, raise mean λ, and increase the COV. The NCHRP507 report text 5
showed the EOID frequency of occurrence histogram of the 99 piles, and Fig. 1 visually displays both EOID and 6
BOR histograms from this study together for comparison. 7
8
FIGURE 1 λ Histograms at EOID and BOR for all 179 qualified piles. 9 10
Allen (18) points out the overall “fit” to statistical distributions and the extreme tail shape fit will both 11
dictate the COV and partly control the differences between First Order Second Moment (FOSM) and random 12
number Monte Carlo-derived φ values (discussed later). The most accurate Monte Carlo-based calibration fit results 13
are driven by the lower portion of the λ distribution, where resistance predictions are unconservative and the risk of 14
failure is higher. 15
A pile blow count-based BOR/EOID set-up ratio (SR) breakdown was examined for piles that used the 16
same hammer on restrike to help identify possible reported blow count keystroke entry errors. A large majority of 17
the 179 case histories had consistently low SRs (< 5) which are highly unlikely to contain any errors. Of the four 18
extreme cases with SR > 30, having ratios of 32, 48, 63, and 166 and high probability of error, two are from Utah in 19
highly sensitive clays, which are mismatched to the stable soil types in the remainder of the dataset. All four piles 20
were flagged and do not feature in any analysis for φ calibration. Thus, the total number of valid cases for φ 21
calibration dropped to 175. The final statistical parameters for the 175 qualified case histories, broken down by soil 22
type, are shown in Table 3, for assumed normal distributions. 23
A statistical breakdown was performed using the input tiers to help assess if clear trends existed and to 24
confirm the usefulness of the tier criteria. At EOID for the 55 piles in Tier 1, the λ and COV statistics were 1.63 and 25
0.62, respectively, while Tier 1 plus Tier 2a, for 86 piles, showed no change in λ or COV. Tier 1 plus Tier 2a plus 26
Tier 2b for all 175 piles gave λ and COV values of 1.56 and 0.71, respectively. The BOR statistics showed very 27
little change in all tier separate combinations. Trends displayed on the EOID and BOR analysis suggested that 28
adding Tier 2a to Tier 1 was acceptable and that the combined use of Tier 1 and Tier 2a cases would form an 29
appropriate basis to study ODOT practice scenarios for φ calibration. 30
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TABLE 3 WEAP Based Resistance Statistical Characteristics of the 175 Qualified Cases by Soil Type 32
Soil # of EOID BOR
Type Cases λ s.d. COV λ s.d. COV
Clay 34 1.94 1.42 0.73 1.10 0.61 0.55
Sand 98 1.27 0.66 0.52 0.90 0.46 0.51
Mixed 43 1.90 1.47 0.77 1.12 0.41 0.36
All Soils 175 1.555 1.10 0.71 0.993 0.47 0.47
TRB 2012 Annual Meeting Paper revised from original submittal.
Trevor D. Smith 8
Examination of the respective λ bias change between EOID and BOR conditions reveal the amount of set-1
up which occurred, on average, for all piles in the soil type group. The drop from λ at EOID of 1.555 to λ at BOR of 2
0.993 for piles in all soils illustrates a gain in resistance of approximately 30 percent. 3
4
Blow Count, Restrike Filters, and Load Test Time Filters 5 The WEAP Manual (2) states that during easy driving, < 2 BPI, inaccurate results may occur, and warns against 6
sustained hard driving conditions. Damage to the pile and/or hammer can occur under hard driving conditions, 7
which typically causes an upper range of 15 to 20 BPI to be recommended by the hammer manufacturer. AASHTO 8
(5) also cautions against driving higher than the 10-15 BPI range to avoid damage to concrete and timber piles. 9
Paikowsky et al. (6) reported that for easy driving, the complex interaction and energy loss, due to the high velocity 10
and acceleration displacement of the soil at the pile tip, is impossible to capture accurately. These high and low 11
blow count issues were examined in the database. The database was separated into bins 2 BPI wide, as shown in 12
Fig. 2, to examine the effect of driving conditions on the statistical distribution of experimental bias and to allow 13
direct comparison to the work of Paikowsky et al. As shown in the figure, those piles with BPI less than or equal to 14
2 account for the majority of the overall variability in statistical bias. Based on the variation of bias as a function of 15
BPI, filtering on the basis of hard driving was considered inappropriate and not done. Shown in Fig. 2, for direct 16
comparison to NCHRP507, are the number of cases in each blow count bin range, the mean λ in the range, and the 17
vertical bar in the bin range expressing the +/- 1 s.d., together with the overall 350 cases’ mean λ (recall 175 piles at 18
both EOID and BOR) and overall +/- 1 s.d. dashed line range, all using the NCHRP507 presentation formatting. 19
20
21 FIGURE 2 All EOID and BOR qualified λ values plotted to blow count in 2 BPI intervals. 22
23
AASHTO (3, 4, 5) recommends wait time before restrike (TR) after the EOID as: clean sands at 1 day, silty 24
sands at 2 days, sandy silts at 3-5 days, and clays at 7-14 days. ODOT bridge foundation construction specifications 25
typically require a minimum one-day set-up period before restrike. AASHTO mandates a minimum of five days 26
after EOID before conducting a static load test, referenced as the time to static load test (TST). The times stated by 27
both ODOT and AASHTO were compared to those 64 piles recorded among the 175 piles where both TR and TST 28
were known, and the majority of these cases did not meet both these requirements. Six piles failed ODOT’s typical 29
BOR wait time TR requirement, 16 piles failed AASHTO’s BOR time recommendation, and 48 out of 64 piles 30
failed to wait AASHTO’s recommended required TST after EOID before the static load test was conducted. 31
However, no trends could be detected to help identify any mismatched cases that were either restruck too early and 32
captured too little set-up, or were load tested much later. Without any compelling and consistent trend, all the cases 33
that violated the TST and TR requirements set forth through ODOT and AASHTO were included in φ calibration. 34
TRB 2012 Annual Meeting Paper revised from original submittal.
Trevor D. Smith 9
In summary, no cases were removed at this stage from the dataset for reasons of falling outside any 1
arbitrary s.d. range, 1 or 2 input tier position, or restrike and load test delay timing. However, their influence was 2
studied through ten different scenario data subsets (A to J) for FOSM recalibration, of which five were of interest to 3
ODOT and tagged for additional Monte Carlo calibration. 4
5
RESISTANCE FACTOR CALIBRATION AND RESULTS 6
First Order Second Moment (FOSM) and Calibration Results 7 For this study, ODOT required the resistance factor to be calculated using reliability theory with the FOSM, as well 8
as with the advanced probabilistic Monte Carlo-based method described by Allen et al. (19). The appropriate 9
resistance value to satisfy the inequality of Eq.1 is a function of the bridge’s proportion of live load (LL) to dead 10
load (DL) and the AASHTO-prescribed code load factors, γij. If Qi is the load and γi is the load factor, then “g” is 11
the limit state function represented by the safety margin, defined in Eq. 3 and, if less than zero, failure is predicted. 12
13
0QγRQ)g(R, iin (3) 14
15
The average bias ratio (λ) of the Davisson’s criteria resistance to the WEAP-predicted resistance, found in the 16
scenario set, is used to statistically calculate the φ resistance factor. When the λ bias ratio is taken as lognormally 17
distributed, the FOSM resistance φ can be easily calculated by Eq. 4 for dead and live load sources. In Eq. 4, all 18
load-related statistics are taken at the value most often selected by LRFD researchers, using AASHTO Strength I 19
load combinations, for driven pile studies on redundant pile groups of five or more (β = 2.33). The full set of 20
statistical parameters used in this study for both FOSM and Monte Carlo procedures are shown in parentheses in Eq. 21
4 definitions. The resistance statistics λR and COVR come from the WEAP capacity analysis. 22
23
24
25
222
2
22
111exp
1
1
QLQDRTQL
L
DQD
R
QLQD
L
L
DDR
COVCOVCOVnQ
Q
COV
COVCOV
Q
Q
(4) 26
27
28
29
where: λR, λQD, λQL = bias factor for resistance, dead load (1.05) and live load (1.15) 30
D, L = dead load (1.25) and live load (1.75) factors 31
T = target reliability index (2.33) 32
COVQD, COVQL = Coefficient of Variation of dead load (0.1) and live load (0.2) 33
QD/QL = dead to live load ratio (2) 34
35
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Ten different scenarios, A through J, were designed to study pile capacity statistical filters, input tier 37
differences, outlier definitions, and ODOT practices. The baseline Scenario A contains all 175 qualified piles. 38
Scenarios B to E examine different NCHRP507 filter effects and input tier differences and help draw conclusions on 39
the changes in base λ and COV statistics. Scenarios F to H are designed to focus on ODOT practice. Table 4 shows 40
the FOSM resistance values for each scenario. The baseline Scenario A matched to NCHRP507 (forming the 41
AASHTO earlier recommendations) are both highlighted in Table 4 at EOID, and are very similar, but do illustrate 42
some differences. The parameters under which NCHRP507 generated the FOSM resistance factors most likely used 43
the +/- 2 s.d. outlier cutoff to improve COVs and inflate φ. Further, the original WEAP data (17) appears to have 44
applied a 10 BPI upper blow count “cap” to select acceptable case histories. Neither the 2 s.d. outlier nor the upper 45
blow count cap were used in the 175 piles in Scenario A. This suggests that Scenario A data quality is slightly 46
superior to the 99 piles of the original NCHRP507 work. This reflects the considerable effort the current study 47
expended for the resolution of anomalies and the inclusion of only carefully selected, and well documented, case 48
histories into the Full PSU Master Database. 49
TRB 2012 Annual Meeting Paper revised from original submittal.
Trevor D. Smith 10
The calculated φ resistance factor is often normalized by the λ bias to offer a measure of that method’s 1
efficiency in confirming pile nominal resistance. Measured by φ /λ efficiencies in Table 4, both Scenario A and 2
NCHRP507 suggest using BOR to optimize pile acceptance, but the EOID or BOR decision is much less clear under 3
all other “filtered” scenarios. As expected, the EOID on the broad Scenario A offered the lowest φ and φ /λ 4
efficiency of any in the table (likely due to the poorly defined upper λ tail inflating the COV). Efficiencies on all 5
other scenarios for both EOID and BOR were generally close to twice that reported at EOID by NCHRP507. Of 6
significance is the effect in Scenario C of employing the +/- 2 s.d. NCHRP507 outlier definition. From the direct 7
comparison to Scenario A, the φ factor was inflated 42 percent, from 0.35 to 0.50, for the EOID condition by the 8
removal of extreme tail data at both ends. 9
10
TABLE 4 WEAP FOSM Resistance Values and Efficiencies for β=2.33 at EOID and BOR 11
Model Filter Set
Driving
Case
# of
Piles
Mean
λ s.d. COV
φ
Factor
φ/ λ
Efficiency
NCHRP507
EOID 99 1.656 1.199 0.724 0.36 0.22
BOR1 99 0.939 0.399 0.425 0.39 0.42
Scenario A Tier 1 + 2 EOID 175 1.555 1.102 0.708 0.35 0.23
BOR 175 0.993 0.468 0.472 0.38 0.38
Scenario B Tier 1 + 2a EOID 82 1.685 1.100 0.653 0.43 0.26
BOR 82 1.030 0.447 0.434 0.42 0.41
Scenario C Tier 1 + 2 EOID 163 1.372 0.669 0.488 0.50 0.37
+/- 2 s.d. cut off BOR 165 0.938 0.399 0.425 0.39 0.42
Scenario D Tier 1 + 2, BPI>2 EOID 138 1.269 0.614 0.484 0.47 0.37
BOR 162 0.967 0.459 0.475 0.36 0.38
Scenario E Tier 1 + 2a, BPI>2 EOID 65 1.394 0.603 0.433 0.57 0.41
and +/-2 s.d. BOR 73 0.970 0.397 0.409 0.42 0.43
Scenario F Tier 1 + 2a, BPI>2 EOID 69 1.406 0.596 0.423 0.59 0.42
BOR 79 1.012 0.429 0.424 0.42 0.42
Scenario G Tier 1 + 2a + Tier 2b,
Rank1, BPI>2
EOID 94 1.328 0.564 0.425 0.56 0.42
BOR 114 0.985 0.430 0.437 0.40 0.41
Scenario H Tier 1 + 2a, EOID 58 1.330 0.570 0.429 0.55 0.42
BPI>2 & TR, TST BOR 69 0.974 0.408 0.419 0.41 0.42
Scenario I
Clay & Mixed
Tier 1 + 2a +Tier 2b,
Rank1, BPI>2
EOID 43 1.464 0.595 0.406 0.64 0.44
BOR 56 1.123 0.457 0.407 0.49 0.44
Scenario J
Sands
Tier 1 + 2a+Tier 2b,
Rank1, BPI>2
EOID 51 1.214 0.515 0.424 0.51 0.42
BOR 58 0.852 0.358 0.421 0.36 0.42 1NCHRP507 statistics for BOR is shown in italics as they only appear in the report’s appendix 12
13
Monte Carlo Methods and Results 14 The Monte Carlo procedure discussed by Allen et al. (18, 19) and Allen (20) is considerably more sophisticated and 15
accurate. It requires high-quality probability density functions (PDF). To summarize, the safety margin defines the 16
risk of failure that arises from the fitting of the lower λ bias resistance distribution tail (unconservative predictions) 17
and the upper total load tail. This study incorporated the recommendations offered by Allen et al. using lognormal 18
“best fits” from three fitting approaches: regressed fitting all the case history data points, regressed fitting by 19
dropping data points from the upper λ tail, and finally fitting the lower λ tail by visual adjustment. These procedures 20
use Excel© spreadsheet computation and random number generation of QDL, QLL, and Rn distributions. By iteration 21
the appropriate resistance factor, φ, is found to produce the target reliability index T value. 22
After ODOT review of the Scenario A-J FOSM results, the Monte Carlo reliability method was performed 23
on five selected practice scenarios of interest: A, F, G, J and I. For each of these scenarios, log normal assumption 24
checks by the Anderson-Darling technique, PDF, cumulative distribution function (CDF), and standard normal 25
variable (SNV), for both EOID and BOR driving conditions, were calculated and are reported by Smith et al. (15). 26
Following Allen (20), the last visual adjustment fit of the lower tail was achieved by manipulation of the mean 27
resistance λ and COV from the scenario under consideration to better match the tail. Shown in Figure 3 is the EOID 28
plot on the baseline Scenario A, illustrating the three fitting techniques. Here the improved visual fit to the tail 29
reduced the COV and consequently increased the φ significantly over the fitting to all data points. All three fits are 30
TRB 2012 Annual Meeting Paper revised from original submittal.
Trevor D. Smith 11
presented by Smith et al. (15) for each scenario, but only the final φ results from the more appropriate best visual 1
lower tail fit are presented in Table 5. 2
3
4 5
FIGURE 3 Standard normal variable to λ bias fits for EOID in Scenario A. 6 7
The superiority of the best lower tail fit approach can also be seen in Figure 3. A single, low outlier λ bias data point 8
dominates the Monte Carlo fit to all the data φ (as well as the FOSM φ). This pile had been placed in the low Input 9
Tier 2b and ranked very low in Output Rank, with noted suspicions of an incorrect EOID reported blow count. The 10
much better visual tail fit raised the Monte Carlo-calibrated EOID φ factor in Scenario A by 50 percent compared to 11
the FOSM method results. 12
13
TABLE 5 FOSM and Monte Carlo Best Visual Tail Fit Based φ and φ/λ Efficiencies for β = 2.33 14
Monte Carlo FOSM
Model Filter Set Mean λ S.D. COV φ φ/λ φ φ/λ
Scenario A Tier 1 and Tier 2 EOID 1.38 0.65 0.471 0.54 0.35 0.35 0.23
BOR 0.91 0.41 0.451 0.39 0.39 0.38 0.38
Scenario F Tier 1 + 2a,
BPI>2
EOID 1.38 0.61 0.442 0.59 0.42 0.59 0.42
BOR 0.96 0.41 0.427 0.42 0.42 0.42 0.42
Scenario G Tier 1 + 2a + 2b,
Rank 1, BPI>2
EOID 1.28 0.55 0.430 0.57 0.43 0.56 0.42
BOR 0.96 0.43 0.448 0.41 0.42 0.40 0.41
Scenario I
Clay & Mixed
Tier 1 + 2a + 2b,
Rank 1, BPI>2
EOID 1.23 0.30 0.244 0.83 0.57 0.64 0.44
BOR 1.08 0.45 0.417 0.49 0.44 0.49 0.44
Scenario J Sands Tier 1 + 2a + 2b,
Rank 1, BPI>2
EOID 1.17 0.51 0.436 0.55 0.45 0.51 0.42
BOR 0.82 0.36 0.439 0.36 0.42 0.36 0.42
15
In summary, the previous FOSM results compared to the best visual tail fit Monte Carlo results, and their respective 16
φ/λ efficiencies, is shown in Table 5 for each scenario at both EOID and BOR conditions. 17
18
CONCLUSIONS AND RECOMMENDATIONS 19 This research study has provided resistance factor recalibration statistics from which ODOT can now design 20
implementation guidelines. Implementation into practice must consider a wide range of issues, including: expected 21
set-up in local soils, construction specifications, ensuring uniformity of WEAP analysis, AASHTO code, and agency 22
TRB 2012 Annual Meeting Paper revised from original submittal.
Trevor D. Smith 12
policy. Statistically a driven pile may belong to one, or both, of two categories for the purposes of nominal 1
resistance determination by any dynamic method—at the EOID condition and at the BOR condition. Both of these 2
categories have been shown by all dynamic resistance methods in past studies to possess different mean λ bias and 3
COVs that change the derived φ factor. This study suggests that WEAP, using DRIVEN, under well-defined 4
conditions and with experienced users, is a reliable measure of nominal resistance for a broader array of soil and pile 5
types than had previously been recognized—for both EOID and BOR conditions. Locating new case histories to 6
add to PDLT2000 and DFLTD allowed researchers to produce a database of 322 piles and to record calendar and 7
clock times on 69 cases for restrike and the load test. A large variation in installation conditions and field practice 8
norms exists in the Full PSU Master Database. These include: pile type, soil type, the time to restrike, the time to 9
static test, and the geographic location of the case histories. This inherent variability of national pile driving norms 10
in a broad database of 175 analyzed piles produced representative, generally applicable, resistance φ factor results, 11
suited to ODOT practice. 12
Neither of the two largest source national databases, PDLT2000 or DFLTD, was always correct on every 13
piece of the large amount of source input required for DRIVEN and WEAP. From extensive crosschecking of the 14
two national databases, DFLTD was considered to be the more accurate and more complete. A baseline Scenario A 15
sample set containing 75 percent more piles than used in NCHRP507 for WEAP was established. The sand sites 16
provided 54 percent of the cases, and cohesive soil contribution sites provided 46 percent of the cases. ODOT 17
practice diversity required keeping the scenario qualifications in Table 4 as broad as possible to avoid eroding the 18
statistical quality of the data for WEAP capacity prediction. Scenarios I and J had 56 cohesive and 58 granular soil 19
sites respectively, and both show high set-up resistance gains measured by WEAP. However, EOID and BOR 20
efficiencies expressed by the φ/λ ratio are all similar for the superior Monte Carlo calibration in Scenarios F-J, 21
except the high EOID set-up cases in Scenario I. 22
Narrowing the scenario data range has the penalty of generating a larger number of pile/soil/driving 23
combinations, each requiring separate φ factors. This complicates implementation and reduces the number of cases 24
available for calibration statistics. Scenario G represents the broadest and best inclusive ODOT category for all 25
piles in all soils with 94 case histories used at EOID and 114 used at BOR (20 low blow count piles were removed at 26
EOID by the N > 2 BPI requirement). Based on the results of Scenario G, the EOID Monte Carlo resistance factor φ 27
for all soils and pile types was calibrated to be 0.57, which is over 40 percent higher than that recommended earlier 28
by AASHTO codes (2, 3) and over 10 percent higher than present AASHTO code (5). It also provided a new 29
restrike BOR resistance factor of 0.41. Most past investigators have followed AASHTO φ step increments of 0.05, 30
which leads to recommendations from this study of 0.55 at EOID and 0.4 at BOR. This research built the Full PSU 31
Master Database and has provided baseline statistics to permit more scenario sub-sets to be examined for φ 32
calibration than were conducted and reported here. These scenarios can then include the effects of pile type, use of 33
field observed hammer strokes, and stress wave monitored hammer performance for the derivation of dynamic 34
signal matching resistance φ factors for comparison to those presented here. Input tiers and output ranks should 35
always be employed in LRFD calibration, and for any database calibration work, independent verification from 36
original sources is recommended. This study used DRIVEN to format the WEAP input files and subsequently used 37
default settings to calculate the bearing graph. For implementation by ODOT, careful consideration should be given 38
to a clear delineation of the restrike definitions and the documentation of appropriate WEAP modeling guidelines. 39
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TRB 2012 Annual Meeting Paper revised from original submittal.
Trevor D. Smith 13
ACKNOWLEDGMENTS 1
The author wishes to recognize the invaluable assistance provided by the ODOT Technical Advisory group, as well 2
as the financial support of ODOT, during the course of this study. Special thanks are also extended to student 3
research group members Jaesup Jin, Andy Banas, Max Gummer, and Jane Wallis for their dedicated scholarship and 4
camaraderie. 5
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TRB 2012 Annual Meeting Paper revised from original submittal.
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